Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that are triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media and their application to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact in cardiac arrhythmias.Peer ReviewedPreprin

How random is your heart beat?

We measure the content of random uncorrelated noise in heart rate variability using a general method of noise level estimation using a coarse grained entropy. We show that usually - except for atrial fibrillation - the level of such noise is within 5 - 15% of the variance of the data and that the variability due to the linearly correlated processes is dominant in all cases analysed but atrial fibrillation. The nonlinear deterministic content of heart rate variability remains significant and may not be ignored.Comment: see http://urbanowicz.org.p

Using skewness and the first-digit phenomenon to identify dynamical transitions in cardiac models

Disruptions in the normal rhythmic functioning of the heart, termed as arrhythmia, often result from qualitative changes in the excitation dynamics of the organ. The transitions between different types of arrhythmia are accompanied by alterations in the spatiotemporal pattern of electrical activity that can be measured by observing the time-intervals between successive excitations of different regions of the cardiac tissue. Using biophysically detailed models of cardiac activity we show that the distribution of these time-intervals exhibit a systematic change in their skewness during such dynamical transitions. Further, the leading digits of the normalized intervals appear to fit Benford's law better at these transition points. This raises the possibility of using these observations to design a clinical indicator for identifying changes in the nature of arrhythmia. More importantly, our results reveal an intriguing relation between the changing skewness of a distribution and its agreement with Benford's law, both of which have been independently proposed earlier as indicators of regime shift in dynamical systems.Comment: 11 pages, 6 figures; incorporating changes as in the published versio

Complex patterns of spontaneous initiations and terminations of reentrant circulation in a loop of cardiac tissue

A two-component model is developed that consists of a discrete loop of cardiac cells that circulates action potentials together with a cardiac pacing mechanism. Physiological properties of cells such as restitutions of refractoriness and of conduction velocity are given via experimentally measured functions. The dynamics of circulating pulses and their interactions with the pacer are regulated by two threshold relations. Patterns of spontaneous initiations and terminations of reentry (SITR) generated by this system are studied through numerical simulations and analytical observations. These patterns can be regular or irregular; causes of irregularities are identified as the threshold bistability of reentrant circulation (T-bistability) and in some cases, also phase-resetting interactions with the pacer.Comment: 27 pages, 10 figures, 61 references; A version of this paper (same results) is to appear in the Journal of Theoretical Biology; arXiv V2 adds helpful commments to facilitate reading and corrects minor errors in presentatio

A statistical index for early diagnosis of ventricular arrhythmia from the trend analysis of ECG phase-portraits

This is the author accepted manuscript. The final version is available from IOP Publishing via the DOI in this record.In this paper, we propose a novel statistical index for the early diagnosis of ventricular arrhythmia (VA) using the time delay phase-space reconstruction (PSR) technique, from the electrocardiogram (ECG) signal. Patients with two classes of fatal VA-with preceding ventricular premature beats (VPBs) and with no VPBs-have been analysed using extensive simulations. Three subclasses of VA with VPBs viz. ventricular tachycardia (VT), ventricular fibrillation (VF) and VT followed by VF are analyzed using the proposed technique. Measures of descriptive statistics like mean (µ), standard deviation (σ), coefficient of variation (CV = σ/µ), skewness (γ) and kurtosis (β) in phase-space diagrams are studied for a sliding window of 10 beats of the ECG signal using the box-counting technique. Subsequently, a hybrid prediction index which is composed of a weighted sum of CV and kurtosis has been proposed for predicting the impending arrhythmia before its actual occurrence. The early diagnosis involves crossing the upper bound of a hybrid index which is capable of predicting an impending arrhythmia 356 ECG beats, on average (with 192 beats standard deviation) before its onset when tested with 32 VA patients (both with and without VPBs). The early diagnosis result is also verified using a leave one out cross-validation (LOOCV) scheme with 96.88% sensitivity, 100% specificity and 98.44% accuracy.This work was supported by the E.U. ARTEMIS Joint Undertaking under the Cyclic and person-centric Health management: Integrated appRoach for hOme, mobile and clinical eNvironments—(CHIRON) Project, Grant Agreement # 2009-1-100228

Optogenetic Control of Cardiac Arrhythmias

The regular, coordinated contraction of the heart muscle is orchestrated by periodic waves generated by the heart’s natural pacemaker and transmitted through the heart’s electrical conduction system. Abnormalities occurring anywhere within the cardiac electrical conduction system can disrupt the propagation of these waves. Such dis- ruptions often lead to the development of high frequency spiral waves that override normal pacemaker activity and compromise cardiac function. The occurrence of high frequency spiral waves in the heart is associated with cardiac rhythm disorders such as tachycardia and fibrillation. While tachycardia may be terminated by rapid periodic stimulation known as anti-tachycardia pacing (ATP), life-threatening ventricular fibril- lation requires a single high-voltage electric shock that resets all the activity and restore the normal heart function. However, despite the high success rate of defibrillation, it is associated with significant side effects including tissue damage, intense pain and trauma. Thus, extensive research is conducted for developing low-energy alternatives to conventional defibrillation. An example of such an alternative is the low-energy anti-fibrillation pacing (LEAP). However, the clinical application of this technique, and other evolving techniques requires a detailed understanding of the dynamics of spiral waves that occur during arrhythmias. Optogenetics is a tool, that has recently gained popularity in the cardiac research, which serves as a probe to study biological processes. It involves genetically modifying cardiac muscle cells such that they become light sensitive, and then using light of specific wavelengths to control the electrical activity of these cells. Cardiac optogenetics opens up new ways of investigating the mechanisms underlying the onset, maintenance and control of cardiac arrhythmias. In this thesis, I employ optogenetics as a tool to control the dynamics of a spiral wave, in both computer simulations and in experiments.In the first study, I use optogenetics to investigate the mechanisms underlying de- fibrillation. Analogous to the conventional single electric-shock, I apply a single globally-illuminating light pulse to a two-dimensional cardiac tissue to study how wave termination occurs during defibrillation. My studies show a characteristic transient dynamics leading to the termination of the spiral wave at low light intensities, while at high intensities, the spiral waves terminate immediately. Next, I move on to explore the use of optogenetics to study spiral wave termina- tion via drift, theoretically well-known mechanism of arrhythmia termination in the context of electrical stimulation (e.g. ATP). I show that spiral wave drift can be induced by structured illumination patterns using lights of low intensity, that result in a spatial modulation of cardiac excitability. I observe that drift occurs in the positive direction of light intensity gradient, where the spiral also rotates with a longer period. I further show how modulation of the excitability in space can be used to control the dynamics of a spiral wave, resulting in the termination of the wave by collision with the domain boundary. Based on these observations, I propose a possible mechanism of optogenetic defibrillation. In the next chapter, I use optogenetics to demonstrate control over the dynamics of the spiral waves by periodic stimulation with light of different intensities and pacing frequencies resulting in a temporal modulation of cardiac excitability. I demonstrate how the temporal modulation of excitability leads to efficient termination of arrhythmia. In addition, I use computer simulations to identify mechanisms responsible for arrhyth- mia termination for sub- and supra-threshold light intensities. My numerical results are supported by experimental studies on intact hearts, extracted from transgenic mice. Finally, I demonstrate that cardiac optogenetics not only allows control of excita- tion waves, but also by generating new waves through the induction of wave breaks. We demonstrate the effects of high sub-threshold illumination on the morphology of the propagating wave, leading to the creation of new excitation windows in space that can serve as potential sites for re-entry initiation. In summary, this thesis investigates several approaches to control arrhythmia dy- namics using optogenetics. The experimental and numerical results demonstrate the potential of feedback-induced resonant pacing as a low-energy method to control arrhythmia.2022-01-1

Assessment of the state of health by the measurement of a set of biophysiological signals

The dissertation studies the estimation of the degree of self-similarity and entropy of Shannon of several real electrocardiography (ECG) signals for healthy and non-healthy humans. The goal of the dissertation is to create a starting point algorithm which allows distinguishing between healthy and non-healthy subjects and can be used as a basis for further study of a diagnosis algorithm, necessarily more complex. We used a novel Hurst parameter estimation algorithm based on the Embedded Branching Process, termed modified Embedded Branching Process algorithm. The algorithm for estimation of entropy was based on Shannon‟s entropy. Both algorithms were applied on the spatial distribution of ECG signals in a windowed manner. The studied signals were retrieved from the Physionet website, where they are diagnosed as normal or as having certain pathologies. The results presented for the Hurst parameter estimation allow us to confirm the results already published on the temporal self-similarity of ECG signals, this time for its spatial distribution. We also conclude that the non-self similar signals belong to non-healthy subjects. The results obtained for entropy estimation on the spatial distribution of ECG signals also allowed a comparison between healthy and non-healthy systems. We obtained high entropy estimates both for healthy and non-healthy subjects; nevertheless, non-healthy subjects show higher variability of Shannon‟s entropy than healthy ones.A dissertação estuda a estimativa do grau de auto-semelhança e da entropia de Shannon de vários sinais reais de electrocardiograma (ECG) obtidos em humanos saudáveis e não saudáveis. O objectivo da dissertação é criar um algoritmo inicial que permita distinguir entre indivíduos saudáveis e não saudáveis e que possa ser usado como base para o estudo de um posterior algoritmo de diagnóstico, necessariamente mais complexo. Utilizamos um algoritmo novo para estimativa do parâmetro de Hurst baseado no Embedded Branching Process, denominado algoritmo modified Embedded Branching Process. A entropia foi estimada através da entropia de Shannon. Ambos algoritmos foram aplicados sob a distribuição espacial dos sinais ECG numa forma de janela. Os sinais estudados foram retirados do website Physionet, onde estão diagnosticados como normais ou possuindo uma determinada patologia. Os resultados apresentados para a estimativa do parâmetro de Hurst permitem confirmar resultados já publicados sobre a auto-semelhança temporal dos sinais ECG, desta vez para a sua distribuição espacial. Também se concluí que os sinais não auto-semelhantes correspondem a indivíduos não saudáveis. Os resultados obtidos na estimativa da entropia para a distribuição espacial dos sinais de ECG também permitiram uma comparação entre sistemas saudáveis e não saudáveis. Obtiveram-se estimativas de entropia elevadas quer para indivíduos saudáveis quer para indivíduos não saudáveis; no entanto, os indivíduos não saudáveis mostram uma maior variabilidade da entropia de Shannon em relação aos saudáveis

Filament behavior in a computational model of ventricular fibrillation in the canine heart

The aim of this paper was to quantify the behavior of filaments in a computational model of re-entrant ventricular fibrillation. We simulated cardiac activation in an anisotropic monodomain with excitation described by the Fenton-Karma model with Beeler-Reuter restitution, and geometry by the Auckland canine ventricle. We initiated re-entry in the left and right ventricular free walls, as well as the septum. The number of filaments increased during the first 1.5 s before reaching a plateau with a mean value of about 36 in each simulation. Most re-entrant filaments were between 10 and 20 mm long. The proportion of filaments touching the epicardial surface was 65%, but most of these were visible for much less than one period of re-entry. This paper shows that useful information about filament dynamics can be gleaned from models of fibrillation in complex geometries, and suggests that the interplay of filament creation and destruction may offer a target for antifibrillatory therap